SCALING LIMITS FOR CONTINUOUS OPINION DYNAMICS SYSTEMS

• 成果类型: Article
• 署名作者: Como, Giacomo; Fagnani, Fabio
• 署名单位: Massachusetts Institute of Technology (MIT); Polytechnic University of Turin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP739
• 发表日期: 2011
• 页码: 1537-1567
• 关键词: CONSENSUS; confidence; algorithms; models

摘要

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system's mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.